(m+2)⁴ = ((m+2)²)²
= (m² + 4+ 2m)²
= m⁴ + 8 + 4m² + 8m² + 16m + 4m³ .........( (a+b+c)² = a²+b²+c²+2ab+2bc+2ac)
= m⁴ + 8 + 12m² + 16m + 4m³
33% of the salary = (33/100) * 2575
= 849.75
So the income tax = 849.75 dollars
Answer:
(C)4
Step-by-step explanation:
Given the line: 
The gradient of the line, 
A line perpendicular to the given line will have a gradient, 
(by definition of perpendicularity).
Therefore, a perpendicular line that passes through the point (4,1) is:
Comparing with the slope-intercept form y=mx+x, the slope of the perpendicular line, b=4.
Given the expression:
-x^2+18x-99
to solve by completing squares we proceed as follows:
-x^2+18x-99=0
this can be written as:
-x^2+18x=99
x^2-18x=-99.......i
but
c=(-b/2)²
Hence:
c=(-(-18)/2)²=81
adding 81 in both sides of i we get:
x^2-18x+81=-99+81
factorizing the quadratic we obtain:
(x-9)(x-9)=-18
thus
(x-9)²+18=0
the above takes the vertex form of :
y=(x-k)²+h
where (k,x) is the vertex:
the vertex of our expression is:
(9,18)
hence the maximum point is at (9,18)
NOTE: The vertex gives the maximum point because, from the expression we see that the coefficient of the term that has the highest degree is a negative, and since our polynomial is a quadratic expression then our graph will face down, and this will make the vertex the maximum point.
Answer:
3.5 to 20.5 hours
Step-by-step explanation:
The range of the sine function is -1 to 1, so the range of H will be ...
-8.5 +12 = 3.5
to
8.5 +12 = 20.5
The length of the day varies by 17 hours from 3.5 hours to 20.5 hours.
